Wednesday, March 26, 2014

Day 212 - Stylized Catalan Wireframes

Settings: MakerWare .3mm/low with support-reducing custom slicing profile, on a Replicator 2. We printed each one in a different color with scraps from home and work so that they would be easy to identify. Each model was scaled by a constant that measured the openness of its design, so that together the models would look like a matching set. The wireframe designs were made using Mathematica, MeshLab, and TopMod. Everything in this paragraph is described in detail below.

Technical notes, nomenclature flavor: Which polyhedron is which? Every face of a Catalan solid is the same non-regular polygon, and the prefix of its name describes the kind of face that it has.

Triakis = faces are isosceles triangles arranged in 3-sided pyramids

Tetrakis = faces are isosceles triangles arranged in 4-sided pyramids

Pentakis = faces are isosceles triangles arranged in 5-sided pyramids

Rhombic = faces are rhombi/rhombuses (grammar police line up and fight!)

Didsyakis = faces are scalene triangles

Deltoidal = faces are kites

Pentagonal = faces are irregular pentagons

Technical notes, differentiation and scaling flavors: The following is a key to the Catalan solids pictured above, together with the respective scaling factors as calculated using the algorithm we explained on Day 195:

Technical notes, support flavor: Starting from the "Standard PLA" MakerWare .2mm profile with raft and supports, we changed the settings listed below. This is the same knot/wireframe support-reducing profile that we have used many times before, posted here just so you don't have to go find it:

"roofThickness": 0.5,

"floorThickness": 0.5,

"sparseInfillPattern": "linear",

"infillDensity": 0.2,

"minSpurLength": 0.4,

"doSupport": true,

"doSupportUnderBridges": true,

"supportDensity": 0.1,

"supportExtraDistance": 0.8,

"supportModelSpacing": 0.5,

Technical notes, modeling flavor: The following is the workflow used to obtain these models. Most of this was described in Day 194 but we repeat it here for completeness and to insert the scaling step that we added in Day 195. We'll walk through with the Pentakis Dodecahedron as our example.

Use Mathematica to create the polyhedron and export to STL, and then calculate the scaling factor for the model: